Clay Flower Creation Based on Homotopy Type Theory
Kenji Ohmori, Toshiyasu L. Kunii · 2014
Homotopy type theory, which generalizes equivalence relations at the most abstract level, is a leading edge science in mathematics and computer science. We have revised our design and modeling method using homotopy type theory. The previously proposed method, which is called the incrementally modular abstraction hierarchy (IMAH), has been applied in many fields of computer science and information technologies. IMAH uses set theory on the second highest abstraction level to clarify sets and their components in a developing system. The clarification of sets and components is more accurately accomplished using homotopy type theory because equivalence relations among components are defined more formally and specifically using the homotopy type. The revised IMAH is applied to clay flower creation. Descending the abstraction hierarchy, the process of clay flower creation is embodied by adding additional concrete properties. Functorial databases are generated in conjunction with defining the clay flower creation processes at each abstraction level.